ScalingStacks

Proposition 7.3.2.

Let \(C\) be an \(\mathbb E_{\infty}\)-algebra in a symmetric monoidal \(\infty\)-category \(\mathcal V\), and consider an \(\mathbb E_0\)-algebra morphism in \(\mathcal V_{/C}\), i.e. equivalently a commuting diagram of \(\mathbb E_0\)-algebra morphisms in \(\mathcal V\) as follows Then, we have an equivalence of spaces \[\mathbb T_2^{\mathcal V_{/C}} (f) \simeq \mathbb T^{\mathcal V}_2(f)_{/C},\] where for the latter space we consider \(C\) as equipped with the \(\mathbb A_2\)-structure induced by its \(\mathbb E_{\infty}\)-structure.